SYDNEY, Feb 2 (Reuters) - The euro neared multi-year peaks on Friday as talk of policy tightening in Europe and expectations that inflation is set to gear up boosted borrowing costs globally, a move that sparked a sell-off in Asian equities.

European shares are seen soft, with spread-betters expecting up to a 0.4 percent fall in Germany’s Dax, and smaller dips in France’s Cac, Britain’s FTSE.

Yields on 10-year U.S. Treasuries jumped to a near four-year peak, markedly steepening the curve and squeezing out investors who had feverishly bet on a tighter spread between longer-dated and short-dated yields.

The European Central Bank, for one, is widely expected to end its asset-purchase programme as early as September. That has pushed five-year German Bund yields above zero for the first time since 2015. UK gilt prices also cheapened significantly.

Investors reacted by bidding the euro broadly higher. The single currency stood near a 2-1/2 year top on the yen and a three-year peak on the dollar at $1.2500.

Yet rising U.S. yields have failed to prop up the dollar index, which paused around a three-year trough.

“The trade weighted dollar continued to weaken very broadly in 2018 with the two key pillars being growth strengthening elsewhere in the world, supporting emerging market forex... and central bank divergence narrowing, supporting euro, yen and British pound,” JP Morgan analyst Charles Perrin wrote in a note to clients.

“The currency was also dragged by U.S. politics.”

The United States is witnessing deep partisan political divisions and intra-party squabbles with lawmakers unable to find common ground on most issues. The federal government shut down last month for three days when Republicans and Democrats failed to strike a deal to fund public operations.

The dollar is not far off a 4-1/2 month low against the yen .

The Bank of Japan did its best to stem the rise in borrowing costs, stepping into the market on Friday with a promise to buy as many bonds as it would take to keep yields low.

Investors now await Januray’s U.S. nonfarm payrolls repor for clues on the strength of the labour market.

Nonfarm payrolls probably rose by 180,000 jobs last month after increasing 148,000 in December, according to a Reuters survey of economists. The unemployment rate is forecast to be unchanged at a 17-year low of 4.1 percent.

Bitcoin, the world’s biggest cryptocurrency, continued to tumble after hitting a record high $19,666 in December on the Bitstamp exchange. It was last down 3.4 percent at a more than two-month trough of $8,690.

The digital coin had skidded to its lowest since November, as a Facebook ban on cryptocurrency adverts and a growing regulatory backlash against the nascent market frightened investors.